Ok, so BAM! Mr.Tarrou. The BAM! man. We are going to start taking a look at quantitative
graphs. The ones that we are going to use by far the most in AP Statistics. Not that
they are not all important, but we can't do very much math to categorical data. So most
of our work this year is going to be on quantitative data, numbers, things that we can run through
formulas. I can talk a lot about all of these these graphs. We are probably going to break
these graphs up into individual videos for each type of graph. So I hope that you enjoy
watching them. You might want to pause and write this down if you want an organized set
of notes. Ok, so I think you could have hit the pause button by then:) Here is the deal
with stem plots and we are going to go back to our make believe grades for our two stats
classes and analyze them together. Stem plots. They are best used for small sets of data.
We have that, there is only ten people in the class supposedly:) We can show the shape
of the distribution with a stem plot. They will also allow us to see the data within
that distribution which is a big plus. They can be hard to make. They can be hard to make.
We will talk about that before my 15 minutes are up. The class widths have very little
flexibility. Class widths are like how many pieces of data are within that particular
catagory or class. We don't like to say category, because I don't want to get you mixed up with
categorical variables like gender, or race, or your letter grade of A, B, C, D, or F.
You can't display decimals. We will make up some shoe sizes here in a second and I will
show you how to deal with it. Stem values can have any number of digits, however you
leaves (you will see what I am talking about in a second) can only have one digit at the
most. Stems can be split by two, five, or ten. Ok, so what the heck is a stem and leaf.
We are going to look at this column of grades. Now, in the last video I handled these grades
as categorical data. We used them to determine people's grades of A, B, C, D, and F. Now
I am not going to do that. I am going to use the numbers the way that they sit. Boom, like
that. So I am not going to assign them a letter grade. That means that my numerical values
are not going to be categorical in this example, it is going to be quantitative. Ok, so I am
going to look at my grades here and I want to make a stem plot. We are going to keep
this in white and I am going to do this other side in a minute in blue. Hopefully that shows
up on the camera. And well, I have scores of somewhere in the nineties, eighties, seventies,
and I have the weird 26. Ok, so that means my stem can be two, three, four, five, six,
seven, eight, and nine. Great, here is what we got. 26, so two and six. We have a 71, seven-one, a couple of 77's. We have an
eighty, so there is an 80. Eighty-one, eighty-four, eighty-eight, ninety-three, and ninety-seven.
You see how I am trying to keep these numbers lined up straight. That is important because
I want to see the shape that the numbers create. That is really really important because later
on you are going to learn about standard deviation and this thing called a Normal bell curve.
Basically almost all of the math that we do in AP Statistics is on bell shaped data. And,
if we have an weird outlier that is a major problem. So this outlier with this data, unless
we had a good reason to through it out, well I would be in a world of hurt. Because that
outlier, a number that falls far outside the normal shape of the distribution would cause
major problem with things like mean and standard deviation. You don't really know what those
mean yet because we are just starting in AP Statistics, but or just whatever stats class
you are in. Well, let's say that this number was in there only because the student did
not come in and make up their test yet. It is really not a valid score. So I am giving
you a valid reason why I can toss out that 26. There is just missing test grade, the
kid was absent. Alright, so now we have this stem plot. Well, this is a problem. When you
make a graphical display of data, we need a minimum of five classes. Now I have three
classes here, the nineties, the eighties, and the seventies. I need at least five if
I want to analyze the shape. So, I need to make more rows of numbers. Well that is where
I come in here and I say that class widths have very little flexibility. Well, when you
start a stem plot, you must count by some kind of....like you have to count. Like one,
two, three, four, five. You cannot skip around. You might have noticed that big gap that I
just unfortunately erased between the basic set of data and the outlier. You have to keep
all of those empty rows in there to really see, oh wow that point was way up there and
was an outlier. It was way far away from all the other numbers. So I need to make more
rows of data, and we do that by what is called splitting the stem. So I am going to do....
I have tossed the 26 because that kid just didn't show up that day for the test. I am
going to keep the sixty here and you will understand in a second. So six, six, seven,
seven, eight, eight, nine, nine, and then finally someone over here in the other class
got a 100 percent so I am going to put ten and another ten. Why am I writing each of
these numbers twice? I am splitting the stem by two. We have a base ten number system.
When we count the stem out, we have to count one, two, three, four...ten, eleven, twelve,
thirteen. Our base ten number system can only be divided evenly by two, five, and ten but
we rarely split stems by ten. So this is going to represent numbers between 60 and 64, 65
to 69, 70 to 74, and so on. I am going to erase this because this is not part of our
stemplot, I am just showing you how to read it. When we split the stems up, five pieces
of data can fall in this row, five pieces of data can fall in this row, and so on. When
we split the stem like this, by two, this is what our data looks like for this column
of grades here in white. 71, alright 71, 77 and 77, 80, 81, 84, 88, now this is 80 to
84 so 88 goes down here, 88. 93 and finally 97. Stem plot. It is fairly symmetric. The
peak is in the middle. I am not going to talk about describing distributions today. That is a whole other lesson. I want to make
a back-to-back stemplot. This is a good use of stem plots. It allows you to compare multiple
distributions if they are small sets of data. If they were really big sets of data, it is
going to look like the Matrix with numbers just flying all over the place. So for the
right hand column we have a low of 65, so that goes here. 71, 79, 81, 84, 86, 89, 91,
95, and finally a hundred. Well, we can see that the peak, there is not very many pieces
of data, but there is a little bit of a clump here. There is a little bit higher grades
grades than the other class. The maximum score of a 100 is higher than 97. And, however because
I threw out the 26, that kid that did not show up for their test, it looks like this
period, let's call it period two has a lower minimum score. So here we have a back-to-back
stem plot comparing two periods of grades if you want to call it that. Alright so, I
think that is pretty much it. Back to back stem plots. OH!!! Who is going to know how
to read this outside of a stats class? Every graph you make should have a key. How are
you going to read the grades in this back-to-back stem plot? Well, give somebody an idea of
how to do that if you made the graph. So, let's say seven line one equals 71. So, let's
take a look at how to deal with decimals. Ok, so I stopped just to make sure that I
was going to stay withing my 15 minute limit for Youtube and I also took the time to write
out some shoe sizes. Now we buy shoes by the half size. You know ten, ten and a half, eight,
whatever. So I have some numbers here and they are all in decimals. How am i going to
display these shoe sizes in a stem plot if I am not able to show a decimal? Well, one
way to do that is just drop them. Just drop all the point fives. Well, what if there is
a 6.5? Do you round it off to 7? Well you can, you can round all of these up. Or, you
can go through here, and I am not going to write this for every single one of these numbers,
but let's just say that I came through and I multiplied all those numbers by ten. Well
if you multiply a number by ten, you know, it moves the decimal over one place. I only
have one decimal place anywhere there is a decimal. They only go to the tenths place.
So, if I multiply all those values by ten, ok I will move the decimals, that becomes
65, 65, 70, 70, 75, 75. All of these decimals are going away. I multiplied by ten, so a
size 8 becomes and 80, this is 90, 90. I have a size of ten, so that is a 100, 110, 110,
120, and 130. So now I have these numbers that used to be shoe sizes, but now they are
not. But we are going to, with the use of a key, let somebody know how to read our stem
plot. So that they know that if it says 110, it is really 11.0 or a size 11 shoe. Well
I just got rid of all my decimals so guess what? I am ready to make a graph! So my stem
is going to be, ok I got my last right hand digit are my leaves, so my stem then starts
at six and goes to thirteen. 6, 7, 8, 9, 10, 11, 12, 13, always with a title so this is
shoe sizes that I have looked at. What do I have? I have 65, 65, I got two 70's, two
75's, I got an 80, a couple of 90's, a couple of 95's, I have got 100, 105, a couple of
110's. I keeping my numbers all nice and lined up nice so I can see the shape as well as
just putting the numbers down. I mean, if I don't see the shape this is all pointless.
120 and 130. This is just one example of how to take data that has decimals and display
them in a stem plot. You can round off those decimals, you can multiply by ten or a hundred,
or just round them off... Did I say that? Ok, so we have a stem plot showing the distribution
of shoe sizes that I just happened to make up. And again with the graph you do need a
key. So eight and zero represents a shoe size of 8.0 If you have data that has a very wide
range. Maybe the smallest number is 20 and the largest number is 540, you might just
need to drop off the single digits, the ones digits and just look at the hundreds and tens
place. They can be really a challenge, trying to figure out how to manipulate the data to
have a decent picture. This is why we prefer histograms. But don't skip those stem plots
in you book. Ask your teacher, get some help if find them to be confusing and the certainly
can be. But stem plots show shape, they show data, they are very good for small sets of
data, they are good as in your back-to-back design for comparing distributions. Let's
move on to histograms. WHOOO!!!